Computationally efficient discrete wavelet transform model

In this paper, a computationally efficient time and transform domain model for computing discrete wavelet transform is descried, and the breaking point for the filter length is derived. This result provides a guideline for choosing a computationally efficient model for a given wavelet. The implementation of wavelet transform is computationally intensive, as the number of computations required increases with the number of octaves. Various methods are applied to reduce the number of operations necessary for calculations of wavelet coefficients. Improved computational efficiency of transform domain model is a result of replacing subsequent transformations, decimations, or interpolations and inverse transformations by simple additions or replications of transform values respectively. Computational complexity per octave for transform domain algorithm is compared with the complexity of direct convolution and modified lattice. A modified lattice structure with commuted sampling rate conversion is found to be significantly more efficient than direct convolution model. Transform domain filtering with incorporated sampling rate conversion leads to a computationally efficient model for computing wavelet coefficients for filters of length 20 or longer (longer wavelet), whereas modified lattice results in better efficiency for shorter filter length (shorter wavelet). Simulation results are presented to illustrate this breaking point filter length and tradeoffs between computational complexity of transform domain and lattice model.